An investigation of Residential Insurance Demand-side Reaction Pre- and Post- Natural

Catastrophe A Case for 2010-11 Christchurch Earthquakes

Presenter Richard Mumo UC PhD Student

Supervisor Richard Watt

ABSTRACT

This paper gives an empirical analysis of post-Christchurch earthquakes insurance reactions

using survey data The paper aims to deduce a model framework that explains how the

insurance marketed reacted and the insurance demand for residential property post natural

disaster This study starts by carrying out a descriptive statistical analysis correlation analysis

and simple regression using SPSS to tests the first research hypothesis Next a multinomial

logistic regression model is used to assess the association between a set of household

insurance and natural disaster features that affect the level of insurance coverage while

controlling for some of the characteristics The regression model is employed to survey data

collected from insured homeowner in Christchurch City The paper uses multinomial logistic

regression model to deduce an econometric framework that has dummy independent

variables

My goal is to use these categorical independent variables to explain variation in the

quantitative dependent variable change in the level of coverage used to proxy insurance

demand In the end then the analysis of the demand for residential and contents insurance

using the survey data will not seek to put a specific number on the level of insurance demand

post-Christchurch earthquakes The result of the analysis demonstrates how the demandersrsquo

characteristics significantly contribute to the change in the level of insurance coverage hence

change in insurance demand

KEY Residential Insurance Christchurch Earthquakes Natural Disaster

Page 2 of 45

Introduction

Insurance sector played a very pivotal role in the re-build of Canterbury region after the

devastation quakes of 20102011 This paper is as a result of investigations that we began in

January 2014 to examine the reactions both supply-side and demand-side of the insurance

industry in the wake of these two catastrophes The paper focuses on the demand-side aspect

of residential property insurance coverage The key interests in the demand-side reactions

centres on analysis of the change in the level of insurance coverage and all the variables that

contributes to changes in insurance demand post-loss In this analysis of residential and

contents insurance demand the study does not seek to calculate a specific value on the

demand for insurance post-earthquakes The study will instead seek to first demonstrate how

the amount of premium the property owners a willing to pay in the new contract arrangement

is associated with the property value and the income of the property owner The study goes

further to investigate how various insurance demand variables affect the level of insurance

coverage post-catastrophe using a multinomial logistic regression model Lastly the study

formulates a central research question that investigates how the demand and supply for

residential insurance reacted to changes caused by the quakes This research question is

crucial in understanding how the insurance demanders have adjusted their level of insurance

as a result of the contracts modifications and insurance demand determinants variables

We thus start with simple statistic for determinants of insurance demand and other demand

associated variable to examine whether this variable have significant association with the

some specific household demographic characteristics In essence then the first step is to carry

out a descriptive statistical analysis correlation analysis and simple regression using SPSS to

tests our first research hypothesis The descriptive statistical analysis will be based on results

of Frequencies-tabulations and Crosstabulation Crosstabulation is a powerful technique that

helps to describe the relationships between categorical (nominal or ordinal) variables With

Page 3 of 45

Crosstabulation we can produce statistics such as Observed Counts and ages Expected

Counts and ages Residuals and Chi-Square Chi-Square tests the hypothesis that the row

and column variables are independent without indicating strength or direction of the

relationship

All the analysis will input a set of household independent variable that determines insurance

level coverage a set insurance coverage parameters that determines insurance demand and

supply and the natural disaster characteristics that affect residential insurance coverage

Survey responses to these three combinations of variables are rigorously analysis to examine

how the Canterbury catastrophe has impacted the residential property and contents insurance

industry and how insurance consumers have reacted to these catastrophic events

First is the category of characterises that tells us about the insured individual who want to buy

insurance coverage which includes age income gender education For the two genders we

would like to see how different gender adjusts their insurance level post-disaster So in the

end we would be able to look at for example how female property owner think about

residential insurance compared to their male counterpart property owner categories

Similarly the analysis looks at age categories young middle-aged and old-aged property

owners to identify if there are any age-differences in residential insurance buying

characteristics Rather than using ages in years in the multinomial logistic regression model

we use age dummies to allow for the flexible and non-linear age effects Thus we create

three age dummies 18-40 (for young) 41-60(for middle-aged) and 61 years and older (for

old-aged) ―61 years and olderrsquorsquo is the reference age group Next we look into the education

category so here we would be looking at the differences in education attainment levels and

how these affect the change in coverage level Why we use education level in the survey

questionnaire is because education level is a key demographic determinant that is expected to

have a positive impact on the insurance demand (Dragos 2014) In most academic literatures

Page 4 of 45

the education attainment levels for an individual is used as a proxy for risk aversion however

there are differences in the results obtained for both non-life and life insurance sectors For

example in non-life an individualrsquos education level is positively related to greater risk

aversion Since my analysis puts emphasis on the effects of the education level to the

residential insurance which belongs to non-life insurance sector this study adopts research

opinion that converge towards the proposition education positively influences the insurance

demand for residential property For the purposes of our multinomial logistic regression

model we set three dummy variables high school graduate university graduate and

postgraduate and others When interpreting our regression results we use ―postgraduate and

othersrsquorsquo as the reference education level category

Similar transformation is done to create dummy for all the variables of interest such that we

come-up with a new set of dummy variables that can be regressed in our model Once all this

is done we do not need to put the entire dummy variable into the regression model all at once

Therefore we end-up with primary independent dummy variable of interest grouped in to two

categories a set of household general features that affect the level of insurance coverage

which includes age gender income and property value and specific insurance coverage and

post-natural disaster perceptions that affect how insured make decision and attitude toward

insurance coverage which includes probability of occurrence of natural disaster amount of

premium charged changed in the premium rates change in risk perception and change in the

perception of insurance coverage per dollar post-catastrophe More importantly we can also

look at how age gender and education influence some of the other household characteristics

like income and property value For example it is safe to suggest that a highly educated

middle-aged male who earns more income or own property of high value have different risk

perception than their less educated young-age male

Page 5 of 45

Review of Previous Literature on Post Catastrophe Experience

There is varying evidence of how post-catastrophe experience impacts insurance for demand

(Slovic Kunreuther amp White 1974) was the first to postulate in over-reaction by economic

agents in the aftermath of a new disaster Since then natural disasters have gained attention

because there are increasing findings more recently from (Aseervatham Born Lohmaier amp

Richter 2015 R E Dumm Eckles Nyce amp Volkman-Wise 2015) to show insurance

consumers over-react to the occurrence of a new disaster (Seog 2008) theoretically

demonstrate that catastrophic events leads to increases in insurance demand when there is

increase in public information regarding a disaster(Browne amp Hoyt 2000) analyse effect of

catastrophic events on demand for insurance using state-level from US for a period of 10

years The authors found that higher premium rates post-disaster leads to depressed demand

when considering flood insurance However the authors point that this pattern could be

consistent with the low demand seen prior to a disaster but does not support the increased

demand post-disaster when premium rates are higher

Working on the same US National Flood Insurance Program (Michel‐Kerjan amp Kousky

2010) finds policy limits associated with this flood insurance program are increased and more

policies are purchased after a flood occurs This sends signals that once there is extreme

catastrophic event like heavy floods individuals over-weight the probability of a future flood

and demand more insurance (Gallagher 2010) tries to estimate the change in probability that

occurs in the aftermath of floods using panel dataset of floods and the take-up of flood

insurance in the US The author provides new evidence on how individuals update their

beliefs over an uncertainty of rare events Most importantly they found out that the

consumption of insurance is completely flat in the years before a flood prickle immediately

following a flood and then steadily diminishes to pre-floods level (Camerer amp Kunreuther

1989 Cohen Etner amp Jeleva 2008 Ganderton Brookshire McKee Stewart amp Thurston

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

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Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

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System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 2 of 45

Introduction

Insurance sector played a very pivotal role in the re-build of Canterbury region after the

devastation quakes of 20102011 This paper is as a result of investigations that we began in

January 2014 to examine the reactions both supply-side and demand-side of the insurance

industry in the wake of these two catastrophes The paper focuses on the demand-side aspect

of residential property insurance coverage The key interests in the demand-side reactions

centres on analysis of the change in the level of insurance coverage and all the variables that

contributes to changes in insurance demand post-loss In this analysis of residential and

contents insurance demand the study does not seek to calculate a specific value on the

demand for insurance post-earthquakes The study will instead seek to first demonstrate how

the amount of premium the property owners a willing to pay in the new contract arrangement

is associated with the property value and the income of the property owner The study goes

further to investigate how various insurance demand variables affect the level of insurance

coverage post-catastrophe using a multinomial logistic regression model Lastly the study

formulates a central research question that investigates how the demand and supply for

residential insurance reacted to changes caused by the quakes This research question is

crucial in understanding how the insurance demanders have adjusted their level of insurance

as a result of the contracts modifications and insurance demand determinants variables

We thus start with simple statistic for determinants of insurance demand and other demand

associated variable to examine whether this variable have significant association with the

some specific household demographic characteristics In essence then the first step is to carry

out a descriptive statistical analysis correlation analysis and simple regression using SPSS to

tests our first research hypothesis The descriptive statistical analysis will be based on results

of Frequencies-tabulations and Crosstabulation Crosstabulation is a powerful technique that

helps to describe the relationships between categorical (nominal or ordinal) variables With

Page 3 of 45

Crosstabulation we can produce statistics such as Observed Counts and ages Expected

Counts and ages Residuals and Chi-Square Chi-Square tests the hypothesis that the row

and column variables are independent without indicating strength or direction of the

relationship

All the analysis will input a set of household independent variable that determines insurance

level coverage a set insurance coverage parameters that determines insurance demand and

supply and the natural disaster characteristics that affect residential insurance coverage

Survey responses to these three combinations of variables are rigorously analysis to examine

how the Canterbury catastrophe has impacted the residential property and contents insurance

industry and how insurance consumers have reacted to these catastrophic events

First is the category of characterises that tells us about the insured individual who want to buy

insurance coverage which includes age income gender education For the two genders we

would like to see how different gender adjusts their insurance level post-disaster So in the

end we would be able to look at for example how female property owner think about

residential insurance compared to their male counterpart property owner categories

Similarly the analysis looks at age categories young middle-aged and old-aged property

owners to identify if there are any age-differences in residential insurance buying

characteristics Rather than using ages in years in the multinomial logistic regression model

we use age dummies to allow for the flexible and non-linear age effects Thus we create

three age dummies 18-40 (for young) 41-60(for middle-aged) and 61 years and older (for

old-aged) ―61 years and olderrsquorsquo is the reference age group Next we look into the education

category so here we would be looking at the differences in education attainment levels and

how these affect the change in coverage level Why we use education level in the survey

questionnaire is because education level is a key demographic determinant that is expected to

have a positive impact on the insurance demand (Dragos 2014) In most academic literatures

Page 4 of 45

the education attainment levels for an individual is used as a proxy for risk aversion however

there are differences in the results obtained for both non-life and life insurance sectors For

example in non-life an individualrsquos education level is positively related to greater risk

aversion Since my analysis puts emphasis on the effects of the education level to the

residential insurance which belongs to non-life insurance sector this study adopts research

opinion that converge towards the proposition education positively influences the insurance

demand for residential property For the purposes of our multinomial logistic regression

model we set three dummy variables high school graduate university graduate and

postgraduate and others When interpreting our regression results we use ―postgraduate and

othersrsquorsquo as the reference education level category

Similar transformation is done to create dummy for all the variables of interest such that we

come-up with a new set of dummy variables that can be regressed in our model Once all this

is done we do not need to put the entire dummy variable into the regression model all at once

Therefore we end-up with primary independent dummy variable of interest grouped in to two

categories a set of household general features that affect the level of insurance coverage

which includes age gender income and property value and specific insurance coverage and

post-natural disaster perceptions that affect how insured make decision and attitude toward

insurance coverage which includes probability of occurrence of natural disaster amount of

premium charged changed in the premium rates change in risk perception and change in the

perception of insurance coverage per dollar post-catastrophe More importantly we can also

look at how age gender and education influence some of the other household characteristics

like income and property value For example it is safe to suggest that a highly educated

middle-aged male who earns more income or own property of high value have different risk

perception than their less educated young-age male

Page 5 of 45

Review of Previous Literature on Post Catastrophe Experience

There is varying evidence of how post-catastrophe experience impacts insurance for demand

(Slovic Kunreuther amp White 1974) was the first to postulate in over-reaction by economic

agents in the aftermath of a new disaster Since then natural disasters have gained attention

because there are increasing findings more recently from (Aseervatham Born Lohmaier amp

Richter 2015 R E Dumm Eckles Nyce amp Volkman-Wise 2015) to show insurance

consumers over-react to the occurrence of a new disaster (Seog 2008) theoretically

demonstrate that catastrophic events leads to increases in insurance demand when there is

increase in public information regarding a disaster(Browne amp Hoyt 2000) analyse effect of

catastrophic events on demand for insurance using state-level from US for a period of 10

years The authors found that higher premium rates post-disaster leads to depressed demand

when considering flood insurance However the authors point that this pattern could be

consistent with the low demand seen prior to a disaster but does not support the increased

demand post-disaster when premium rates are higher

Working on the same US National Flood Insurance Program (Michel‐Kerjan amp Kousky

2010) finds policy limits associated with this flood insurance program are increased and more

policies are purchased after a flood occurs This sends signals that once there is extreme

catastrophic event like heavy floods individuals over-weight the probability of a future flood

and demand more insurance (Gallagher 2010) tries to estimate the change in probability that

occurs in the aftermath of floods using panel dataset of floods and the take-up of flood

insurance in the US The author provides new evidence on how individuals update their

beliefs over an uncertainty of rare events Most importantly they found out that the

consumption of insurance is completely flat in the years before a flood prickle immediately

following a flood and then steadily diminishes to pre-floods level (Camerer amp Kunreuther

1989 Cohen Etner amp Jeleva 2008 Ganderton Brookshire McKee Stewart amp Thurston

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 3 of 45

Crosstabulation we can produce statistics such as Observed Counts and ages Expected

Counts and ages Residuals and Chi-Square Chi-Square tests the hypothesis that the row

and column variables are independent without indicating strength or direction of the

relationship

All the analysis will input a set of household independent variable that determines insurance

level coverage a set insurance coverage parameters that determines insurance demand and

supply and the natural disaster characteristics that affect residential insurance coverage

Survey responses to these three combinations of variables are rigorously analysis to examine

how the Canterbury catastrophe has impacted the residential property and contents insurance

industry and how insurance consumers have reacted to these catastrophic events

First is the category of characterises that tells us about the insured individual who want to buy

insurance coverage which includes age income gender education For the two genders we

would like to see how different gender adjusts their insurance level post-disaster So in the

end we would be able to look at for example how female property owner think about

residential insurance compared to their male counterpart property owner categories

Similarly the analysis looks at age categories young middle-aged and old-aged property

owners to identify if there are any age-differences in residential insurance buying

characteristics Rather than using ages in years in the multinomial logistic regression model

we use age dummies to allow for the flexible and non-linear age effects Thus we create

three age dummies 18-40 (for young) 41-60(for middle-aged) and 61 years and older (for

old-aged) ―61 years and olderrsquorsquo is the reference age group Next we look into the education

category so here we would be looking at the differences in education attainment levels and

how these affect the change in coverage level Why we use education level in the survey

questionnaire is because education level is a key demographic determinant that is expected to

have a positive impact on the insurance demand (Dragos 2014) In most academic literatures

Page 4 of 45

the education attainment levels for an individual is used as a proxy for risk aversion however

there are differences in the results obtained for both non-life and life insurance sectors For

example in non-life an individualrsquos education level is positively related to greater risk

aversion Since my analysis puts emphasis on the effects of the education level to the

residential insurance which belongs to non-life insurance sector this study adopts research

opinion that converge towards the proposition education positively influences the insurance

demand for residential property For the purposes of our multinomial logistic regression

model we set three dummy variables high school graduate university graduate and

postgraduate and others When interpreting our regression results we use ―postgraduate and

othersrsquorsquo as the reference education level category

Similar transformation is done to create dummy for all the variables of interest such that we

come-up with a new set of dummy variables that can be regressed in our model Once all this

is done we do not need to put the entire dummy variable into the regression model all at once

Therefore we end-up with primary independent dummy variable of interest grouped in to two

categories a set of household general features that affect the level of insurance coverage

which includes age gender income and property value and specific insurance coverage and

post-natural disaster perceptions that affect how insured make decision and attitude toward

insurance coverage which includes probability of occurrence of natural disaster amount of

premium charged changed in the premium rates change in risk perception and change in the

perception of insurance coverage per dollar post-catastrophe More importantly we can also

look at how age gender and education influence some of the other household characteristics

like income and property value For example it is safe to suggest that a highly educated

middle-aged male who earns more income or own property of high value have different risk

perception than their less educated young-age male

Page 5 of 45

Review of Previous Literature on Post Catastrophe Experience

There is varying evidence of how post-catastrophe experience impacts insurance for demand

(Slovic Kunreuther amp White 1974) was the first to postulate in over-reaction by economic

agents in the aftermath of a new disaster Since then natural disasters have gained attention

because there are increasing findings more recently from (Aseervatham Born Lohmaier amp

Richter 2015 R E Dumm Eckles Nyce amp Volkman-Wise 2015) to show insurance

consumers over-react to the occurrence of a new disaster (Seog 2008) theoretically

demonstrate that catastrophic events leads to increases in insurance demand when there is

increase in public information regarding a disaster(Browne amp Hoyt 2000) analyse effect of

catastrophic events on demand for insurance using state-level from US for a period of 10

years The authors found that higher premium rates post-disaster leads to depressed demand

when considering flood insurance However the authors point that this pattern could be

consistent with the low demand seen prior to a disaster but does not support the increased

demand post-disaster when premium rates are higher

Working on the same US National Flood Insurance Program (Michel‐Kerjan amp Kousky

2010) finds policy limits associated with this flood insurance program are increased and more

policies are purchased after a flood occurs This sends signals that once there is extreme

catastrophic event like heavy floods individuals over-weight the probability of a future flood

and demand more insurance (Gallagher 2010) tries to estimate the change in probability that

occurs in the aftermath of floods using panel dataset of floods and the take-up of flood

insurance in the US The author provides new evidence on how individuals update their

beliefs over an uncertainty of rare events Most importantly they found out that the

consumption of insurance is completely flat in the years before a flood prickle immediately

following a flood and then steadily diminishes to pre-floods level (Camerer amp Kunreuther

1989 Cohen Etner amp Jeleva 2008 Ganderton Brookshire McKee Stewart amp Thurston

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

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Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 4 of 45

the education attainment levels for an individual is used as a proxy for risk aversion however

there are differences in the results obtained for both non-life and life insurance sectors For

example in non-life an individualrsquos education level is positively related to greater risk

aversion Since my analysis puts emphasis on the effects of the education level to the

residential insurance which belongs to non-life insurance sector this study adopts research

opinion that converge towards the proposition education positively influences the insurance

demand for residential property For the purposes of our multinomial logistic regression

model we set three dummy variables high school graduate university graduate and

postgraduate and others When interpreting our regression results we use ―postgraduate and

othersrsquorsquo as the reference education level category

Similar transformation is done to create dummy for all the variables of interest such that we

come-up with a new set of dummy variables that can be regressed in our model Once all this

is done we do not need to put the entire dummy variable into the regression model all at once

Therefore we end-up with primary independent dummy variable of interest grouped in to two

categories a set of household general features that affect the level of insurance coverage

which includes age gender income and property value and specific insurance coverage and

post-natural disaster perceptions that affect how insured make decision and attitude toward

insurance coverage which includes probability of occurrence of natural disaster amount of

premium charged changed in the premium rates change in risk perception and change in the

perception of insurance coverage per dollar post-catastrophe More importantly we can also

look at how age gender and education influence some of the other household characteristics

like income and property value For example it is safe to suggest that a highly educated

middle-aged male who earns more income or own property of high value have different risk

perception than their less educated young-age male

Page 5 of 45

Review of Previous Literature on Post Catastrophe Experience

There is varying evidence of how post-catastrophe experience impacts insurance for demand

(Slovic Kunreuther amp White 1974) was the first to postulate in over-reaction by economic

agents in the aftermath of a new disaster Since then natural disasters have gained attention

because there are increasing findings more recently from (Aseervatham Born Lohmaier amp

Richter 2015 R E Dumm Eckles Nyce amp Volkman-Wise 2015) to show insurance

consumers over-react to the occurrence of a new disaster (Seog 2008) theoretically

demonstrate that catastrophic events leads to increases in insurance demand when there is

increase in public information regarding a disaster(Browne amp Hoyt 2000) analyse effect of

catastrophic events on demand for insurance using state-level from US for a period of 10

years The authors found that higher premium rates post-disaster leads to depressed demand

when considering flood insurance However the authors point that this pattern could be

consistent with the low demand seen prior to a disaster but does not support the increased

demand post-disaster when premium rates are higher

Working on the same US National Flood Insurance Program (Michel‐Kerjan amp Kousky

2010) finds policy limits associated with this flood insurance program are increased and more

policies are purchased after a flood occurs This sends signals that once there is extreme

catastrophic event like heavy floods individuals over-weight the probability of a future flood

and demand more insurance (Gallagher 2010) tries to estimate the change in probability that

occurs in the aftermath of floods using panel dataset of floods and the take-up of flood

insurance in the US The author provides new evidence on how individuals update their

beliefs over an uncertainty of rare events Most importantly they found out that the

consumption of insurance is completely flat in the years before a flood prickle immediately

following a flood and then steadily diminishes to pre-floods level (Camerer amp Kunreuther

1989 Cohen Etner amp Jeleva 2008 Ganderton Brookshire McKee Stewart amp Thurston

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

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Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

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Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

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Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

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Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

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Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

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20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

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Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

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Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

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Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 5 of 45

Review of Previous Literature on Post Catastrophe Experience

There is varying evidence of how post-catastrophe experience impacts insurance for demand

(Slovic Kunreuther amp White 1974) was the first to postulate in over-reaction by economic

agents in the aftermath of a new disaster Since then natural disasters have gained attention

because there are increasing findings more recently from (Aseervatham Born Lohmaier amp

Richter 2015 R E Dumm Eckles Nyce amp Volkman-Wise 2015) to show insurance

consumers over-react to the occurrence of a new disaster (Seog 2008) theoretically

demonstrate that catastrophic events leads to increases in insurance demand when there is

increase in public information regarding a disaster(Browne amp Hoyt 2000) analyse effect of

catastrophic events on demand for insurance using state-level from US for a period of 10

years The authors found that higher premium rates post-disaster leads to depressed demand

when considering flood insurance However the authors point that this pattern could be

consistent with the low demand seen prior to a disaster but does not support the increased

demand post-disaster when premium rates are higher

Working on the same US National Flood Insurance Program (Michel‐Kerjan amp Kousky

2010) finds policy limits associated with this flood insurance program are increased and more

policies are purchased after a flood occurs This sends signals that once there is extreme

catastrophic event like heavy floods individuals over-weight the probability of a future flood

and demand more insurance (Gallagher 2010) tries to estimate the change in probability that

occurs in the aftermath of floods using panel dataset of floods and the take-up of flood

insurance in the US The author provides new evidence on how individuals update their

beliefs over an uncertainty of rare events Most importantly they found out that the

consumption of insurance is completely flat in the years before a flood prickle immediately

following a flood and then steadily diminishes to pre-floods level (Camerer amp Kunreuther

1989 Cohen Etner amp Jeleva 2008 Ganderton Brookshire McKee Stewart amp Thurston

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 6 of 45

2000 Kirsch 1986 McClelland Schulze amp Coursey 1993 Palm 1995 Shanteau amp Hall

1992) analysis on insurance demand reactions in the aftermath of a catastrophe they suggest

that insureds have the belief that the probability of an event is lowered when that event has

already occurred (Papon 2008) study also suggests that prior risk occurrences influence

subsequent insurance choices Although several papers make the case for risk perceptions

affecting natural disaster insurance decisions (Braun amp Muermann 2004 Kousky Luttmer

amp Zeckhauser 2006 Kunreuther 1984 Kunreuther Meszaros Hogarth amp Spranca 1995

Manson 2006 Michel‐Kerjan amp Kousky 2010) shows that there is very little empirical

work on how insurance demanders use their heuristic probability rule to update their past

insurance coverage (Born amp Viscusi 2006) finds that major catastrophes may reduce the

quantity of insurance written because of the higher rates and insurance rationing as well as

exiting of firms from the market Similarly (West amp Lenze 1994) argues that heavily

flooding hurricanes are exemplified by relatively low insurance coverage

In the analysis of determinants for insurance demand (Browne amp Kim 1993) explains that a

higher level of education is a good proxy to measure the risk aversion Thus more risk-averse

individuals due to higher education attainment positively influence the demand for non-life

products (J Francois Outreville 1996) also supports the view expressed by (Browne amp Kim

1993) In the same line (Dzaja 2013) suggested that education increases individuals risk

aversion and encourages people to demand insurance (Treerattanapun 2011) points out that

high education attainment increases the understanding of risk and threats to financial

stability helping the understanding of insurance benefits (Park amp Lemaire 2012) analysis on

82 countries for a period of 10 years also found a positive relation between education and

non-life insurance demand levels (Ofoghi amp Farsangi 2013) demonstrated a significant and

positive relationship between risk aversion and auto insurance demand in which those with

insurance knowledge are more risk-averse

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 7 of 45

Research Hypothesis

Based on findings of previous studies and empirical observation of the New Zealand

insurance industry in the aftermath of Canterbury two major earthquakes we construct three

research hypotheses The aftermath of Canterbury disasters necessitated the insurance and the

re-insurance companies to modify the residential insurance contracts The insured are

supposed to nominate a sum insured to which the insurer is liable to pay in the event of

another disaster This means the premium rates will be heavily depended on value of sum

insured as nominated by the insured This contract modification motivates the first research

hypothesis

Hypothesis I There is positive association between annual premium the insurance

demanders are willing to pay to fully protect their property and contents

through insurance mechanism their property value and their annual

household income

This particular research hypothesis tests if indeed the household income and the property

value affect how much premium an insurance demander will be willing to pay to protect their

property In general the test will show whether there is any association between the three

variables by carrying out a descriptive analysis In the end then this study using the above

hypothesis will establish how the catastrophes affect expenditure on insurance coverage for a

predetermine sum insured and hence demand for residential and contents insurance coverage

The hypothesis draws from the findings in the prior literature For example in (Tooth 2015)

the implied income elasticity for the take-up of house insurance is around 002 suggesting

that (after controlling for other factors) a 1 per cent increase in income would only result in a

001 to 002 per cent increase in the likelihood a household has house insurance cover The

other important findings is by (Showers amp Shotick 1994) which analysed data from the 1987

US Consumer Expenditure Survey to assess the effects of age income and household

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 8 of 45

characteristics on total insurance expenditure Of note they found insurance expenditure to be

positively related to income age and size of household and that the marginal importance of

income to be greater for small households

Hypothesis II Demographic characteristic of households positively influences the

demand for residential insurance cover in the aftermath of a Natural

Disaster

Individual insurance consumersrsquo risk aversion is highly affected by some of the major

demographic characteristics like value of insured asset income age amongst other features

The degree of risk aversion is a key determinant of insurance demand this study uses the

demographic characteristic of households living in Canterbury region to proxy risk aversion

Our demographic characteristic of household includes age gender level of education

incomes and property value

In the insurance literature the level of risk aversion is hypothesised to be positively

correlated with insurance consumption of an individual Numerous empirical studies (Beck amp

Webb 2003 Browne amp Kim 1993 Hwang amp Gao 2003) have demonstrated a positive and

significant relationship between insurance demand and the level of education which would

hence imply a higher level of education may lead to a greater degree of risk aversion and

greater awareness of the necessity of insurance coverage However in macroeconomic and

cross-section studies this hypothesis does not always hold and it cannot always be suggested

that there is a positive correlation between risk aversion and the level of education For

instance(J Franccedilois Outreville 2014) survey of the relationship between risk aversion and

education shows negative relationship Implying that higher education leads to lower risk

aversion that in turn leads to more risk‐taking by highly‐educated individuals

(Aliagha Jin Choong Nadzri Jaafar amp Ali 2014) examines the role of income level and

education level while purchasing flood insurance for residential properties Their study finds

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 9 of 45

that the propensity to purchase flood insurance increases significantly with income levels

while education level does not make much difference They suggest that the increase is likely

as a result of property owners suffering greater losses of wealth (accumulated savings from

income) from the previous catastrophic floods that increases their risk aversion With (Guiso

amp Paiella 2008) pointing that households that face income uncertainty or suffered loss of

income from severe natural disaster show evidence of a greater degree of risk aversion

Similarly (Showers amp Shotick 1994) used US consumer expenditure survey to assess the

effects of age income and household characteristics on total insurance expenditure they

found insurance expenditure to be positively related to income age and size of household and

that the marginal importance of income to be greater for small households

Hypothesis III Change in risk perception influences the demand for residential insurance

cover in the aftermath of a Natural Disaster

Insurers normally assess risk by making best estimates of the frequency and severity of a

hazard using statistical techniques or catastrophe models However expertrsquos generated

perception risk information often has small influence on decision making about risk by lay

person (Kunreuther Novemsky amp Kahneman 2001) (R E Dumm et al 2015 Papon

2008 Viscusi 1985) suggests that individuals often use heuristics simple rules when they

are assessing risk Thus individuals may judge an event as risky if it is easy to imagine or

recall for example individuals who have experienced the Christchurch earthquakes may find

it easier to imagine that the disaster could happen again in the future and therefore feel a

higher perceived risk than individuals without this experience Thus with this analysis we are

in a position to study how this sentimental feeling is used to judge the level of risks

Obviously we expect people in the affected region to have a higher risk perception If natural

hazard are associated with negative feeling which can have been caused or reinforced by

experiences of damage caused by natural hazard then we hypothesis this will drive the

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 10 of 45

demand for residential insurance up and this will be reflected in our proxy increase in the

level of insurance coverage

Research Question I How the supply and demand for residential insurance reacts to

changes in the aftermath of a catastrophic event

So far using the intertemporal model for two period (pre- and post-loss) our findings shows

that demand for insurance after loss increases and if no loss demands for insurance falls

Research Question One seeks to go further using empirical data from the survey to show

how variables that affect demand have changed post-Canterbury earthquakes To examine the

post-catastrophe insurance supply and demand reactions we set out four variables that prior

literature suggests have an immediate reaction from natural disaster The four set of variable

are used to explore out if there are any general reaction that in the end affect the insurance

demand or insurance supply

The first variable examined the perception by the survey respondents towards the probability

of loss from another earthquake Since many insurance demanders do not mathematical

compute the level of risk they use heuristic rule as a strategy that reduces the complex tasks

of assessing probabilities and predicting values to simpler judgmental operations (Raschky amp

Weck-Hannemann 2007 Rothschild amp Stiglitz 1992 Slovic Fischhoff Lichtenstein

Corrigan amp Combs 1977)

The second variable examines the supply-side reaction from demanderrsquos perspective The

survey question set-out to investigate whether natural disaster impacts the supply of insurance

to the affected market This looks at the availability of insurance coverage post-quakes

Previous literature suggests catastrophes suppress insurance supply (Parker amp Steenkamp

2012) studies immediately after the Canterbury quakes finds that A few insurers were in the

process of exiting the New Zealand market or limiting their exposures For households and

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 11 of 45

businesses they also find restricted availability of insurance to cover construction of new

buildings hampered investment and the rebuild process

The third variable examines how insured property value reacts to catastrophes The study on

this variable want to reveal out if there are any changes in property value post natural disaster

and how the property value impacts on the insurance premium It seems reasonable to

postulate that rational property buyer behaviour in regard to residential insurance should

reflect price-efficient policies relative to disaster risk exposure In the end it is possible to

show in general how the property value and insurance premium have impacted insurance

demand Natural disaster literatures try to outline the various social and economic impacts of

different disasters by examining changing property values in disaster prone areas These

studies have essentially had the same goal of modelling disaster impacts to property value

but their methods have differed and the findings have often been contradictory While it

would seem reasonable to hypothesize that an event like floods or earthquake would have a

negative effect on property value this has not always been supported by the literature (R

Dumm Nyce Sirmans amp Smersh 2012) model implies that increases in insurance premiums

due to a re-evaluation of expected loss following a natural disaster would lower property

values (Parker amp Steenkamp 2012) finds that property prices suggested that the loss of

residential properties outstripped the loss of population generating some excess demand for

housing around Canterbury Rents for new rental contracts had increased by 18 in

Christchurch since the end of 2010 compared with the 7 increase nationwide

The fourth variable examines how household expenditure on insurance changed in the

aftermaths of the quakes

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 12 of 45

Research Method

Our Modelling Framework

Our modelling framework is based on the logistic regression analysis model In regression

analysis the common discussion is about how to find a relationship between endogenous

variable iy and a set of explanatory variables

1 1 nx x x

expressed as 1 1( )i i ny f x x x

If the outcome of endogenous variable iy is a dichotomy with values 1 and 0 and say define

( )i i nip E y x which is now the probability that iy is 1 given some value of the

explanatory variable x

Then a logistic regression model can be derived from a linear probability models as follow

0 1 1 2 2 i i i n nip x x x

Since the logistic model assumes that the natural log of the odds ( 1)p p

is a linear function

of the explanatory variables This can be written in the form

0 1 1 2 2[ ( 1)] i i i i n ni iln p p x x x+

Thus using (equation 2) the multinomial logistic regression model for this study is expressed

in form

1 1 2 2 i i i i n ni ix x xy =α +

The multinomial logistic regression model used is generally effective where the dependent

variable is composed of a polychromous category having multiple choices The basic concept

was generalized from binary logistic regression as proposed in (Agresti amp Kateri 2011

Starkweather amp Moske 2011)

In this study our model framework aims to explain the demand for residential property and

contents insurance post natural disaster In our survey data this is measured by the proxy

changed in level of insurance coverage When we replace the parameters of multinomial

logistic regression equation above with our survey variables then the modelling equation to

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 13 of 45

estimate the changed in the level of insurance coverage (used to proxy demand for

insurance)is given as

1

2

3

4

5

Change in level of

insurance coverage= α+ β (measure of INCOME)

+ β (change in PREMIUM post - loss)

+ β (NATURAL DISASTER consideration before purchase of property)

+ β (measure of PROPERTY VALUE to be insured)

+ β (change in LEVEL OF RIS

6

error term

K post - loss)

+ β (dummy household demographic features AGEGENDER amp EDUCATION

+

To this end then the above modelling equation is used to assess the association between

household insurance and natural disaster features that affect the level of insurance coverage

Thus why our analysis uses multinomial logistic regression model which can be a useful tool

for modeling where the dependent variable is a discrete set of more than two choices

(Agresti 1996) The multinomial logistic regression model used in this study estimates the

effect of the individual variables on the probability of changing the level of insurance

coverage

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 14 of 45

Data

This study uses data from online survey conducted through random sampling of employees

from four major public organisations University of Canterbury Christchurch Polytechnic

Institute of Technology (ARA Institute) Christchurch Airport and Christchurch Womens

Hospital all these organisations are domiciled in Canterbury region This organisation where

selected to provide the regionrsquos representative estimates of residential properties affected by

the 201011 quakes The survey was designed for the primary purpose of collecting data on

pre- and post- catastrophe reactions specifically focusing on purchase of Home Insurance

The sample of interest consisted of those homeowners insured with the local private

insurance companies The survey aimed to collect individual-level information that literature

suggests should be important determinants of home insurance demand In compiling this

dataset we intended to examine the influence of each of these factors on home insurance

demand in a multinomial logistic regression framework

Detailed Data Collection Process

The process of putting together a survey questionnaire began in the early months of 2015

After a series of refinement editing and taking in to account all the comments from varying

stakeholders the first draft of the questionnaire was ready by May 2015

All data collection activities necessitated conformity to standard procedures for conducting

household surveys In this light the process sought survey approval (ie sampling survey

design and reporting methodologies) from the University of Canterbury ethics committee

which was cleared by June 2015

In the aftermaths of the quakes many homeowners left their damaged homes to new suburbs

or relocated to other cities Online survey was hence considered as the most efficient survey

method The Universityrsquos Qualtrics survey tool which is jointly administered by Academic

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 15 of 45

Services Group and the Centre for Evaluation and Monitoring was the preferred survey tool

Most importantly the use of a number survey tools such as SurveyMonkey is discouraged

for official University research purposes (To delete)

The University Communication Office distributed the qualtric survey link on June 28 2015

via the University weekly e-newsletter on my behalf However this did not yield anticipated

results only got a paltry 7 responses from the University Communications invitation Next I

took a more direct approach and emailed the staff directly appealing to them of their research

support by taking time to complete the survey The second survey invitations included the

Christchurch Polytechnic Institute of Technology Christchurch Airport and Christchurch

Women Hospital whose emails were gathered from publicly available websites In total 1600

emails were sent between September and November 2015 some of which I had no means of

ascertaining their email address validity The participation rate in the second data

gathering exercise was better an additional 229 responses was received by end of December

2015 In total the survey was closed with 254 responses The next stage entailed sorting and

cleaning the compiled data A close look into all the completed log-ins found that 24

of questionnaires were started but not totally completed In addition 18

participants responded via my email expressing their ineligibility to participate 3 all their

claims were covered by EQC 8 didnrsquot own residential property and 7 were not residing in

Christchurch during the earthquakes In the end 212 responses out of 254 have the required

information for analysis

Pilot Tests

One pilot test was conducted to ensure that the survey design and materials would capture the

data necessary to meet the survey objectives First focus groups of 10 emails were sent to

examine the respondent rate and factors that affect participation in the post-catastrophe

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 16 of 45

survey or might hinder accurate completion of the survey Focus group results were used to

revise survey questionnaire and other respondent materials prior to the full survey Based on

the pilot test results improvements were made in the invitation email and minor text changes

were made to the questionnaire title

Results and Discussions

This section gives summary of results and discussions of descriptive analysis and

multinomial logistic regression to answer our research hypothesis

In order to investigate the association between annual premiums insurance demanders are

willing to pay to fully protect their homes property value and annual household income this

study employed descriptive analysis using SPSS

The results of the analysis are reported in Tables 1- 8

Table 1 Correlation analysis for Hypothesis I (Premium versus Income)

Annual

income

Amount of premium willing to pay per

annum to fully protect property and contents

through insurance

Annual income Pearson Correlation 1 233

Sig (2-tailed) 001

N 208 205

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Pearson Correlation 233 1

Sig (2-tailed) 001

N 205 208

Correlation is significant at the 001 level (2-tailed)

If we refer to the first hypothesis the computed correlation coefficient value for premium

versus income is reported in Table 1 as 0233 and the associated p-value is 0001 Because the

observed p-value is less than alpha value (ie p-value = 0 001˂ 005) the results are

considered statistically significant While the data is significant at the 005 level the

computed coefficient value is closer to 0 than to +1 Therefore with results R = 0233 N =

211 p-value = 0001 it can be concluded that the study finds a weak positive linear

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 17 of 45

relationship between the annual premium an insurance demanders are willing to pay and their

income The weak relationship of premium and income is not surprising given that the

analysis excludes other variables such as the value of contents and age that are closely

correlated with income The results for income versus premium are consistent with the

analysis on house insurance in that controlling for other factors income by itself should not

be a major determinant of demand for insurance cover or the amount of premium demanders

are willing to pay This argument can be furthered by looking into a contingency table

summary of income distribution against the hypothetical annual premium options This

crosstabulation analysis depicts the number of times each of the possible category

combinations occurred in sample data on the two variables (annual premium an insurance

demander is willing to pay and the annual household income)

Across all income categories the vast majority of the sample respondent 424 observed

that they are willing to pay annual premium in the rage of $900 - $1200 to fully protect their

property and contents through insurance mechanism 317 of the sample respondents are

willing to pay annual premium in the rage of above $1200 205 of the sample is willing

to pay annual premium in the rage of $600 - $900 and tiny minority 54 of the sample

is willing to pay annual premium in the rage of below $600 The profile for income

categories below $14000 which is (000 000 00 and 00 ) has been dropped out

of the analysis The profile for income categories $14001 - $48000 is (214 74 357

and 357 ) for income categories $48001 - $70000 is (75 358 373 and

194 ) and for income categories above $70000 is (24 137 460 and 379 )

which essential do not departs from the total ages profile of (44 205 434 and

317 )

Table 2 shows that the willingness to pay premium option $901 - $1200 among the sample

insurance demanders on income bracket $48001 - $70000 and premium option above $1200

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 18 of 45

among the insurance demanders on income bracket above $70000 are relatively higher than

other premium options and salary brackets in this study Most importantly in this survey is

that the vast majority of the respondents preferred maximum annual premium in the regions

$901 - $1200 The same conclusions can also be justified by looking at the adjusted residuals

(-05 -10 and 13) across all income brackets across this premium option

Table 2 Crosstab of the amount premium insurance demander is willing to pay per annum to fully

protect property and contents through insurance mechanism Annual household income

Annual income

Total

b) $14001 -

$48000

c) $48001 -

$70000

d) Above

$70000

Amount of premium

willing to pay per

annum to fully

protect property and

contents through

insurance

a) Below

- $600

Count 3 5 3 11

within Amount of premium 273 455 273 1000

within Annual income 214 75 24 54

Adjusted Residual 28 9 -23

b) $600 -

$900

Count 1 24 17 42

within within Amount of

premium 24 571 405 1000

within Annual income 71 358 137 205

Adjusted Residual -13 38 -30

c) $900 -

$1200

Count 5 25 57 87

within Amount of premium 57 287 655 1000

within Annual income 357 373 460 424

Adjusted Residual -5 -10 13

d) Above

$1200

Count 5 13 47 65

within Amount of premium 77 200 723 1000

within Annual income 357 194 379 317

Adjusted Residual 3 -26 24

Total Count 14 67 124 205

within Amount of premium 68 327 605 1000

within Annual income 1000 1000 1000 1000

This argument is based on the fact that under the null hypothesis that the two variables are

independent the adjusted residuals will have a standard normal distribution ie have a mean

of 0 and standard deviation of 1 So an adjusted residual that is more than 196 (20 is used

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 19 of 45

by convention) indicates that the number of cases in that cell is significantly larger than

would be expected if the null hypothesis were true with a significance level of 005 An

adjusted residual that is less than -20 indicates that the number of cases in that cell is

significantly smaller than would be expected if the null hypothesis were true In summary the

adjusted residual is a measure of how significant the cells (observed minus expected value)

are to the chi-square value Therefore when the cells are compare the adjusted residual

makes it easy to see which cells are contributing the most to the value and which are

contributing the least Looking at the Crosstab the computed Pearson Chi-Square statistics

(26672) and the associated p-value (0001) figures alone we could reject the null hypothesis

and report that there is a significance association between the annual premium the insurance

demanders are willing to pay to fully protect their property and contents through insurance

mechanism and the annual household income

Table 3 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their annual household income

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-

Square 26672a 6 000 000b 000 001

Likelihood Ratio 24022 6 001 001b 000 001 Fishers Exact

Test 24005 000b 000 000

Linear-by-Linear

Association 11092c 1 001 002b 001 002 001b 000 002

N of Valid Cases 205

a 4 cells (333 ) have expected count less than 5 The minimum expected count is 75

b Based on 10000 sampled tables with starting seed 1993510611

c The standardized statistic is 3330

From Table 3 the p-value based on the Chi-square test is the tail area to the right of 26672

from a chi-square distribution with 6 degrees of freedom The computed p-value is 0001

which is the basis for the rejection of the null hypothesis However the Chi-square test does

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 20 of 45

not give any information on how the two variables are related or how strong the relationship

is

The statistics in Table 4 provides a measure of the strength of the association between the two

variables In this case the low significant values for the Contingency Coefficient indicates

that there is some relationship between the two variables (annual premium insurance

demanders are willing to pay to fully protect property and contents through insurance

mechanism and annual household income)

Table 4 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and annual household

income

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal

by

Nominal

Contingency Coefficient

339 000 000c 000 001

Interval by

Interval

Pearsons R 233 075 3416 001d 002c 001 002

Ordinal by

Ordinal

Spearman Correlation 242 070 3559 000d 001c 000 001

N of Valid Cases 205

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 1993510611

d Based on normal approximation

The value of the test statistics is small 0339 an indication that the positive relationship

between the two variables is a fairly moderate one In the previous an attempt was made to

make the contingency coefficient to always range between 0 and 1 but not all conform to this

(Janson amp Vegelius 1979 Mehta amp Patel 1989)

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 21 of 45

Figure 1 Distribution of annual premium insurance demanders are willing to pay Vs Annual income

Figure 1 gives a clear picture of the sample distribution of annual premium insurance

demanders is willing to pay to fully protect their residential property through insurance

mechanism against annual household income

Similarly if we refer to the first hypothesis the computed correlation coefficient value for

premium versus property value is reported in Table 5 The computed correlation coefficient

value is 0536 and the associated p-value is 0000 Because the observed p-value is less than

alpha value (ie p-value = 0 000˂ 005 so reject H0) the results are statistically significant

Therefore with results R = 0536 N = 211 p-value = 0000 it can be concluded that the

study finds a strong positive linear correlation between the annual premium an insurance

demander is willing to pay to fully protect hisher property and contents through insurance

mechanism and the property value

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 22 of 45

Table 5 Correlation analysis for hypothesis I (premium versus property value)

Amount of premium willing to pay per

annum to fully protect property and

contents through insurance

Approximate

property value

Amount of premium willing to

pay per annum to fully protect

property and contents through

insurance

Pearson Correlation 1 536

Sig (2-tailed) 000

N 208 204

Approximate property value Pearson Correlation 536 1

Sig (2-tailed) 000

N 204 207

Correlation is significant at the 001 level (2-tailed)

This argument can be furthered by looking into a contingency table summary of income

distribution against the hypothetical annual premium options This crosstabulation analysis

depicts the number of times each of the possible category combinations occurred in sample

data on the two variables (annual premium an insurance demander is willing to pay and the

annual household income)

Table 6 Crosstab of the amount of premium willing to pay per annum to fully protect property and

contents through insurance Approximate property value

Approximate property value

Total

Below

$30000

$300000 -

$400000

$400000 -

$500000

$500000 -

$600000

$600000 -

$700000

Above

$700000

Amount of

premium willing

to pay per annum

to fully protect

property and

contents through

insurance

a) Below

- $600

Count 5 3 0 0 0 0 8

within Amount of

premium 625 375 00 00 00 00 1000

within property

value 333 150 00 00 00 00 39

Adjusted Residual 61 27 -14 -14 -13 -17

b) $600 -

$900

Count 9 7 9 7 4 6 42

within Amount of

premium 214 167 214 167 95 143 1000

within property

value 600 350 231 171 111 113 206

Adjusted Residual 39 17 4 -6 -15 -19

c) $900 -

$1200

Count 1 10 22 19 19 16 87

within Amount of

premium 11 115 253 218 218 184 1000

within property

value 67 500 564 463 528 302 426

Adjusted Residual -29 7 19 5 14 -21

d)

Above

$1200

Count 0 0 8 15 13 31 67

within Amount of

premium 00 00 119 224 194 463 1000

within property

value 00 00 205 366 361 585 328

Adjusted Residual -28 -33 -18 6 5 46

Total Count 15 20 39 41 36 53 204

within Amount of

premium 74 98 191 201 176 260 1000

within property

value 1000 1000 1000 1000 1000 1000 1000

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 23 of 45

Looking at the Crosstab the computed Pearson Chi-Square statistics from Table 7 the Chi-

square test value is the tail area to the right of 97127 from a chi-square distribution with 15

degrees of freedom The computed p-value is 000 which is the basis for the rejection of the

null hypothesis

Table 7 Test for association between annual premium insurance demanders are willing to pay to fully

protect property and contents through insurance mechanism and their property value

Value Df

Asymp

Sig (2-

sided)

Monte Carlo Sig (2-sided) Monte Carlo Sig (1-sided)

Sig

99 Confidence

Interval

Sig

99 Confidence

Interval

Lower

Bound

Upper

Bound

Lower

Bound

Upper

Bound

Pearson Chi-Square 97127a

15 000 000b 000 000

Likelihood Ratio 89384 15 000 000b 000 000

Fishers Exact Test 75984 000b 000 000

Linear-by-Linear

Association

58346c

1 000 000b 000 000 000b 000 000

N of Valid Cases 204

a 9 cells (375 ) have expected count less than 5 The minimum expected count is 59

b Based on 10000 sampled tables with starting seed 2000000

c The standardized statistic is 7638

The statistically significant statistics contingency coefficient value of 0568 and correlation

coefficient value of 0536 indicates a very strong positive association between the annual

premium insurance demanders are willing to pay and the approximate property value

Table 8 Measure of the strength of association between annual premium insurance demanders are

willing to pay to fully protect property and contents through insurance mechanism and property value

Value

Asymp

Std Errora

Approx

Tb

Approx

Sig

Monte Carlo Sig

Sig

99 Confidence Interval

Lower Bound

Upper

Bound

Nominal by

Nominal

Contingency

Coefficient 568 000 000c 000 000

Interval by

Interval

Pearsons R 536 053 9026 000d 000c 000 000

Ordinal by

Ordinal

Spearman

Correlation 492 058 8031 000d 000c 000 000

N of Valid Cases 204

a Not assuming the null hypothesis

b Using the asymptotic standard error assuming the null hypothesis

c Based on 10000 sampled tables with starting seed 2000000

d Based on normal approximation

Although hypothesis does not examine the influence of the property value on insurance take-

up rates for the analysis of the annual premium insurance demanders are willing to pay and

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 24 of 45

the property value an increase in the value of property increases average level of insurance

coverage holding all else constant Figure 2 gives a clear picture of the sample distribution of

annual premium insurance demanders is willing to pay to fully protect their residential

property through insurance mechanism against approximate property value

Figure 2 Distribution of annual premium insurance demanders are willing to pay Vs property value

Findings I

From the results and conclusions of the tests on research hypothesis I (premium versus

income) the study finds that There is a fairly moderate relationships between the amounts of

premium insurance demanders are willing to pay and their income The vast majority 424

of the sampled insurance demanders elected to pay an annual maximum premium in the

region of $900 to $1200

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 25 of 45

From the results and conclusions of these tests on research hypothesis I (premium versus

property value) the study finds that there is a strong positive linear association between the

annual premiums an insurance demander is willing to pay to fully protect hisher property and

contents through insurance mechanism and the property value Itrsquos observed that the vast

majority 424 of the sampled insurance demanders elects to pay an annual maximum

premium in the region of $900 to $1200 Holding all other factors constants this hypothesis

finds that the vast majority 585 of those willing to pay premium above $1200 have

property valued above $700000 the vast majority 564 of those willing to pay premium

options $900 - $1200 have property valued between $400000 - $500000 and the vast majority

of those willing to pay premium options $600 ndash 900 and below $600 have property valued

above $300000

Next if we refer to the second hypothesis demographic characteristic of households would

positively influences the demand for residential insurance cover in the aftermath of a natural

disaster and the third hypothesis change in risk perception influences the demand for

residential insurance cover in the aftermath of a natural disaster The objective here is to run a

regression analysis with the level of insurance coverage as our dependent variable so as to

address the two research hypothesis To achieve this objective we bring a list of different

explanatory independent variables together to run a multinomial logistic regression we report

output results as seen in Table 9-13

In general the output result shows that the effect of a number of the explanatory variables is

not-statistically significantly For example one statistically significant predictor variable

increase in level of coverage due to higher risk affects more significantly the level of

coverage than other predictor variable with p-value 000 This can also be seen from the

actual proportion (929) of those who perceive high risk as the cause of change in the level

of insurance coverage

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 26 of 45

More importantly the initial run of the model shows that when looked as a whole the model

is significant with a p-value 000 and chi-square statistics 40824 This implies that at least

one or more of the regression coefficients in the model are not equal to zero When looking at

the results of the regression all variable may not be significant few of them are significant

but because we are predicting it is very important for us to keep all the variable of the mode

Even when most of the regression variables are not statistically significant it would be wrong

to remove them from the model This is because even if they may not have the explanatory

power within the model some may have predictive powers in the overall regression model

To run the multinomial logistic regression we selected question number fifteen from the

survey questionnaire that captures the change in the level of insurance coverage as our

dependent variable and a set of thirteen independent variables from a set of eight survey

questions

We use the nomreg command in the SPSS programme to estimate a multinomial logistic

regression model The regression output for the increase in the level of insurance coverage

dummy against a range of explanatory dummy variables as shown in the case processing

summary on Table 9 gives the response propotions where the selected explanatory variables

have been transfer to dummy variables

NOMREG Q15_1 (BASE=LAST ORDER=ASCENDING) BY Q1_1 Q1_2 Q2_1 Q3_1

Q3_2 Q4_1 Q4_2 Q8_1 Q8_2 Q9_1 Q13_1 Q13_2 Q16_2a

CRITERIA CIN(95) DELTA(0) MXITER(100) MXSTEP(5) CHKSEP(20)

LCONVERGE(0) PCONVERGE(0000001) SINGULAR(000000001)

MODEL

STEPWISE=PIN(05) POUT(01) MINEFFECT(0) RULE(SINGLE)

ENTRYMETHOD(LR) REMOVALMETHOD(LR)

INTERCEPT=INCLUDE

PRINT=PARAMETER SUMMARY LRT CPS STEP MFI

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 27 of 45

Table 9 Case Processing Summary

N Marginal Percentage

Change in Level of Coverage 000 125 592

100 86 408

Young Age 000 194 919

100 17 81

Middle Age 000 82 389

200 129 611

Male 000 89 422

100 122 578

High School Graduate 000 194 919

100 17 81

University Graduate 000 144 682

200 67 318

Low Income 000 199 943

100 12 57

High Income 000 22 104

200 189 896

Lower Property Value 000 176 834

100 35 166

Medium Property Value 000 128 607

200 83 393

Natural Disaster consideration before purchase 000 85 403

100 126 597

Increase in premium rates post- earthquakes 000 199 943

100 12 57

Decrease in premium rates post- earthquakes 000 28 133

200 183 867

Increase in level of coverage due to higher risk 000 196 929

100 15 71

Valid 211 1000

Missing 0

Total 211

Subpopulation 99a

a The dependent variable has only one value observed in 76 (768) subpopulations

The data summary in Table 9 shows that 592 of the sampled insurance demanders

reported an increase in the level of their coverage with 929 attributing this change as a

result of higher perception of risk and 943 attributing the change as a result of increase in

premium rates post- earthquakes This points that the change in the level of insurance

coverage might not necessary mean a change in demand rather an increase in coverage level

due to incease in price of insurance coverage post-catastrophe

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 28 of 45

Table 10 Model Fitting Information

Model

Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square Df Sig

Intercept Only 189558

Final 148734 40824 13 000

Table 10 indicates the parameters of the regression model for which the model fit is

calculated With ―Intercept Onlyrsquorsquo we describes a model that does not control for any

predictor variables and simply fits an intercept to predict the outcome variable in this case

our intercept in this case is 189558 With ―Finalrsquorsquo we describe a model that includes the

specified predictor variables by an iterative process that maximizes the log likelihood of the

outcomes as seen in the outcome variable So by including the predictor variables and

maximizing the log likelihood of the outcomes as seen in the data the final model should

improve upon the intercept only model The new -2(Log Likelihood) value associated with

the final model is 148734 From this two values (intercept only and final) we could compute

the associated Chi-Square test statistics which tells us that at least one of the predictors

regression coefficients is not equal to zero in this model the value is 40824 The small p-

value from the LR test 000 lt 00001 would lead us to conclude that at least one of the

regression coefficients in the model is not equal to zero The parameter of the chi-square

distribution used to test our null hypothesis is 13 as defined by the degrees of freedom in

table

Logistic regression does not have an equivalent to the R-squared that is found in OLS

regression however many researchers have tried to come up with one

Table 11 Pseudo R-Square

Cox and Snell 176

Nagelkerke 237

McFadden 143

Table 11 reports the three pseudo R-squared values of our multinomial logistic regression

model There are a wide variety of pseudo R-squared statistics which can give contradictory

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 29 of 45

conclusions (Bruin 2006) Because these statistics do not mean what R-squared means in

OLS regression the proportion of variance of the response variable explained by the

predictors their interpretation will be ignored for now

Table 12 Likelihood Ratio Tests

Effect

Model Fitting

Criteria Likelihood Ratio Tests

-2 Log

Likelihood of

Reduced

Model Chi-Square Df Sig

Intercept 148734a 000 0

Young Age 149436 703 1 402

Middle Age 148761 027 1 869

Male 148850 116 1 733

High School Graduate 149306 572 1 450

University Graduate 148857 124 1 725

Low Income 148894 161 1 688

High Income 148780 046 1 830

Lower Property Value 148734 000 1 983

Medium Property Value 148824 091 1 763

Natural Disaster consideration before purchase 149747 1013 1 014

Increase in premium rates post- earthquakes 156206 7473 1 006

Decrease in premium rates post- earthquakes 154517 5783 1 016

Increase in level of coverage due to higher risk 174500 25767 1 000

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model

The reduced model is formed by omitting an effect from the final model The null hypothesis is that all

parameters of that effect are 0

a This reduced model is equivalent to the final model because omitting the effect does not increase the degrees

of freedom

In order to estimate our regression model we used 13 explanatory variables from 8 survey

questions as reflected in the overall model fit in Table 10 The estimated chi-square test

statistics is reported in Table 12

Table 13 reports the parameter estimates for the explanatory variables coefficient and the

associated p-values

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 30 of 45

Table 13 Parameter Estimates

Change in Level of Coveragea B Std Error Wald Df Sig Exp(B)

95 Confidence Interval for

Exp(B)

Lower

Bound

Upper

Bound

00 Intercept -21297 1867 130175 1 000

[Young Age=00] 531 632 706 1 401 1701 493 5874

[Young Age=100] 0b 0

[Middle Age=00] 060 365 027 1 869 1062 519 2173

[Middle Age=200] 0b 0

[Male=00] -110 323 116 1 733 896 476 1687

[Male=100] 0b 0

[High School

Graduate=00] -490 661 549 1 459 613 168 2239

[High School

Graduate=100] 0b 0

[University

Graduate=00] 125 357 124 1 725 1134 563 2281

[University

Graduate=200] 0b 0

[Low Income=00] 404 1011 160 1 689 1498 207 10861

[Low Income=100] 0b 0

[High Income=00] 159 747 045 1 831 1172 271 5064

[High Income=200] 0b 0

[Lower Property

Value=00] -010 486 000 1 984 991 382 2566

[Lower Property

Value=100] 0b 0

[Medium Property

Value=00] -108 360 091 1 763 897 443 1818

[Medium Property

Value=200] 0b 0

[Natural Disaster

consideration before

purchase=00]

327 326 1005 1 016 1386 732 2625

[Natural Disaster

consideration before purchase=100]

0b 0

[Increase in premium rates post-

earthquakes=00]

2176 1053 4267 1 039 8808 1118 69416

[Increase in premium

rates post-

earthquakes=100]

0b 0

[Decrease in premium

rates post- earthquakes=00]

2498 1207 4284 1 038 12160 1142 129503

[Decrease in premium rates post-

earthquakes=200]

0b 0

[Increase in level of

coverage due to higher

risk=00]

18728 000 1 1359759525

41 1359759525

41 1359759525

41

[Increase in level of

coverage due to higher risk=100]

0b 0

a The reference category is 100 b This parameter is set to zero because it is redundant

We recall that an important feature of the multinomial logistic model is that it estimates

1p models where p is the number of levels of the outcome variable In this case the

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 31 of 45

model treats no change in insurance coverage level as the reference group and therefore

estimated a model for increase in insurance coverage level relative to no change in insurance

coverage level Therefore since the parameter estimates are relative to the reference group in

each dummy variable our standard interpretation of the regression results in Table 13 is that

for a unit change in the predictor variable the logistic of outcome significance level relative

to the reference group is expected to change by its respective parameter estimate (which is in

log-odds units) given the variables in the model are held constant For example the intercept

value gives the multinomial logistic estimate for increase in insurance coverage level relative

to no change in insurance coverage level when the predictor variables in the model are

evaluated at zero Thus the logistic for probability of increase in insurance coverage level

relative to no change in insurance coverage level is -21297 Table 13 also gives the standard

errors of the individual regression coefficients for the model estimates the Wald chi-square

test that the null hypothesis estimates equals zero the degrees of freedom for each of the

variables included in the model (Note for each of these variables the degree of freedom is 1

unless where the variable is redundant) the p-values of the coefficients within a given model

which tells us that the null hypothesis that a particular predictors regression coefficient is

zero given that the rest of the predictors are in the model the odds ratios for the predictors

which indicates how the risk of the outcome falling in the comparison group compared to the

risk of the outcome falling in the reference group changes with the variable in question and

the 95 Confidence Interval (CI) for Exp(B) - This is the CI for an individual multinomial

odds ratio given the other predictors are in the model for outcome significance level relative

to the referent group

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 32 of 45

Findings II

If we refer to the research hypothesis II and III the regression analysis finds that from the

survey data 592 of the sampled insurance demanders reported an increase in the level of

their coverage with 929 attributing the change as a result of change in perception of risk

and 943 attributing the change as a result of increase in premium rates post- earthquakes

The results of the regression give likelihood ratio chi-square of 40824 with an associated p-

value lt 00001 which tells us that our regression model as a whole fits significantly better

than an empty model (ie a model with no predictor variables) Thus we conclude age

gender education income property value natural disaster premium rates and risk

perceptions substantially affect the level of insurance coverage post-natural disaster From the

parameter estimates of our regression model vulnerability to natural disaster change in

premium rates and change in risk perception are the most statistically significant explanatory

variables These parameters would positively influence the demand for residential insurance

cover in the aftermath of a natural disaster However it is difficult to show how much of the

change in insurance level can be attributed to increase in premium In such case change in

premium rates would not reflect demand of insurance coverage

The vast majority of insurance consumers who had previously filed claims for natural disaster

reported to have higher risk perception This is in line with the numerous research findings

that postulate that higher risk perception is recorded from those who have prior experience of

catastrophes than those who have not To address our research question how the supply and

demand for residential insurance reacts to changes in the aftermath of a catastrophic event

we plot figures that depict how the catastrophes have impacted the demand-side We have so

far proved demand for insurance post-loss increases using a theoretic inter-temporal

insurance model Using the four most pronounced variables of interest the results of our

analysis are given below

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 33 of 45

The first result gives reports for the change in the perception of probability of loss The

respondents were asked to identify their perception (including actual experience observations

and also what they have heard from others) in relation to their current residential property

and contents insurance policy how the probability of loss from another earthquake had

changed

Figure 3 Probability of loss from another earthquake

In line to previous research findings that suggests demand would increase with an increase in

risk 441 of the sample perceives the probability of loss from another quake to have

increased while 237 of the sample perceives the probability to have decreased and 322 were in

neutral position regards the perceived post-quake probability of loss It can be further argued looking

into the respondent observation on the level of insurance coverage that the 408 of the sample who

elected to voluntarily increase level of past insurance converge and the 929 of the who elected the

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 34 of 45

change in the coverage to have be motivated by higher risk are of as a rational responses to perceived

increase in the probability of loss from another earthquake

The second plot presented gives results for the reaction in relation to the availability of

insurance coverage On Figure 4 results of plot of the survey responses on the availability of

insurance coverage post-quake is seen above The survey question here examines

respondentrsquos perception and rating on overall changes in the availability of insurance

coverage to insurer residential property and contents in the aftermath of 2010 and 2011

Canterbury earthquakes

Figure 4 Availability of insurance coverage

The vast majority 706 indicated that availability of insurance coverage has decreased 256

of the sample respondents were neutral as to whether the availability of insurance coverage

has increased or decreased and only tiny minority 38 observed that insurance availability

has increased post-quakes When this question is examined with the data on CPI insurance

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 35 of 45

components inflation for households throughout New Zealand (source from the Statistic New

Zealand) and the responses on post-quake premium changes as seen in Figure 6 below the

results suggest that the Christchurch earthquakes had a strong effect on the residential

property and contents insurance coverage Figure 6 reports an insurance component inflation

of residential property raising at about 40 high

Figure 6 CPI insurance components inflation for households and for businesses throughout New Zealand

To shed more light these results can further be jointly examined with the responses on cases

where an insurance provider consciously declined to offer insurance coverage to protect

property against any potential future risk for some customers On the question regarding

whether an insurance provider declined to offer insurance coverage of 24 respondents who

provided specific comments on reasons for insurance coverage declined 11 states that the

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 36 of 45

cover was declined because of the following specific reasons as stated by the provider of the

insurance cover

Claimed on the driveway damage and now they will not cover the driveway to the

same extent as before

Did not have a kitchen

Immediately after the February earthquake the company wasnt taking on any new

insurance

New building many companies wouldnt undertake new policies

No companies are taking on new customers

No response to request for quote

Not stated

Paid-out not repaired therefore uninsurable except for public liability yet fit to live in

Received pay-out Company unwilling to offer 3rd

party fire cover

Too soon after the September 2010 earthquake and

Was not providing contents cover for Canterbury

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 37 of 45

The above comment depicts a pragmatic reactions experience by the insured which clearly captures the actual

supplydemand reactions and relationship of the insurance market post catastrophe

Figure 7 Case where an insurance cover was declined

The survey results on the availability of coverage and cases where some insurance demanders

where turned away sheds light on the experiences and opinions of people purchasing

coverage post-quakes The study can therefore generally infer that following a catastrophe

insurance providers approach the market more cautiously

The third reaction that this study analysis is the change in property value (insured assets) As

reflected in our survey questionnaire the perceived change insurance coverage per dollar of

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 38 of 45

property insured is an important parameter to understand how the insured feels about return

for every dollar spent to purchase insurance cover

Most of the respondent as seen on Figure 8 observed that there was a sharp increase in

property value after the earthquakes 37 observed the property value to have increased

while 28 observed some slightly increase in property value In general it can be said that

707 observed an upward change in property value while 147 observed no change in

property value with the same percentage observing downward change

Figure 8 Insured property value post-earthquakes

The forth plot give changes in the expenditure on insurance in the aftermath of catastrophic loss Past

studies shows that consumers would choose insurance policy that yields the highest benefit

per additional dollar of insurance expenditure holding other factors constant Thus the

questions regarding how the respondents have generally changed their expenditure on

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 39 of 45

insurance depict how quakes affected the total expenditure associated with insurance policies

This study finds a whopping majority 957 have in general increased the total amount of

money they spend on insurance post-quakes Only 33 observed to have decreased their

spending on insurance while a 09 neither increased nor decreased the amount of money

spent on insurance

Figure 9 Expenditure on insurance

Further analysis of insurance expenditure as the dependent variable with incomes and the

value of property to insure reveal that there is a strong association between these variable as

shown in the results of hypothesis one The survey finds expenditure on insurance to be

consistent with the literature on the choice to insure In general the results of the study on

money spent on insurance when linked with key household characteristics indicates that

insurance expenditure generally increases with and greater incomes greater value of

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 40 of 45

property to insure To quote (McCormick amp Kempson 1998) ―hellipexpenditure on home

contents insurance accounted for 20 per cent of income for the poorest fifth of households

compared to just 05 per cent for the richest fifthhelliprdquo

Moreover Figure 9 and 10 gives a possible suggestion a relationship between the increase in

premiums post-quakes and the increase in insurance expenditure With the respondents in

both cases observing increments above 91 it can be argued that most of the increase in

insurance expenditure might have been majorly due to increased premium rates rather than

change in level of coverage

Figure10 Change in premium rate

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 41 of 45

Findings III

In addressing our research question this analysis finds that the vast majority of insurance

consumers update their perception of catastrophic risk Especially those who have had a

recent experience with natural disaster events with policyholders involved in Canterbury

quakes claims reporting 441 higher perception of a likelihood of loss from another similar

disaster Our results are in fact in line with heuristic rule which is supported by numerous

literatures On the insurance policy availability our study finds that there was a noticeable

decline and moratorium of new insurance contracts The vast majority of respondents at 706

reported a decline in availability of new insurance contracts New policyholders found it

difficult to meet the new insurance requirement and policy exclusions

The catastrophic on Christchurch affected stability of many building with many of the

property owners be temporally displaced or the suburb declared as red zone Our survey

shows that the displacement pushed the demand for houses which resulted to increase in rents

and property value with 707 of the respondents reporting an increase in property value

Having shown insurance expenditure is positively related to income and property value this

study finds a whopping majority at 957 reporting an increase in the total amount of money

spend on insurance policy in the aftermath of the earthquakes catastrophe

Conclusions

The results of the first hypothesis suggest that the value of homes is highly correlated with

income (and can be used to proxy wealth) collectively influence the amount of premium the

insurance demanders are willing to pay and the level of insurance coverage These two

parameters are an indication of expected losses which would suggest that those with higher

income and higher property values would purchase higher coverage amounts Using the

finding from this study we conclude that an increase in an individualrsquos income should have

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 42 of 45

no major effect on demand if insurance is actuarially fair More often however positive

loading exists reflecting transaction costs and possibility of adverse selection In such cases

the direction of the effect depends on whether an increase in income increases losses and on

whether the insurance demander has increasing or decreasing absolute risk aversion

Our findings suggest that perceptions play an important role in insurance decisions to

voluntarily change their insurance cover Thus if the insurance demander perceives a higher

possibility of natural disaster then they adjust their coverage appropriately They confirm this

studyrsquos hypothesis that a householdrsquos decision to increase decrease or no change of the

insurance coverage level post-loss is influenced unequally by perceptions relating to

occurrence of natural disaster in the future Perceptions relating to the risk post-loss and

considerations of the existence of disasters and the market insurance premiums adjustments

are found to be the most significant and important parameter estimates Thus insurance

providers and the government regulators need to recognize individual perceptions regarding

risk and anyother market policy modification to be a key factor in post-disaster insurance

demand reactions and to invest in understanding them in their design of interventions to

stimulate more demand for insurance coverage as well as protect the insurance market from

ruin

However this study acknowledges that recognizing and addressing the entire past catastrophe

reaction and the factors that shape them will only provide a partial solution to the complex

problem of the aftermaths of natural disaster and the necessary rebuild with sufficient

insurance compensation measures thereof

As the composition of the Christchurch dwellers evolves as the city gets back to normality

changes in individual characteristics will affect the demand for insurance for example

individuals who have experienced the Christchurch earthquakes may find it easier to imagine

that the disaster could happen again in the future and therefore feel a higher perceived risk

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 43 of 45

than individuals without this experience Maximizing these important subjective judgements

in decision making will require understanding all these multiple factors involved using a

variety of methodological approaches and addressing them through multifaceted

interventions

Page 44 of 45

Reference

Agresti A amp Kateri M (2011) Categorical data analysis Springer

Aliagha U Jin T Choong W Nadzri Jaafar M amp Ali H (2014) Factors affecting flood

insurance purchase in residential properties in Johor Malaysia Natural Hazards and Earth

System Science 14(12) 3297-3310

Aseervatham V Born P Lohmaier D amp Richter A (2015) Putting everything under the same

umbrellandashHazard-specific supply reactions in the aftermath of natural disasters Munich Risk

and Insurance Center Working Paper(25)

Beck T amp Webb I (2003) Economic demographic and institutional determinants of life insurance

consumption across countries The World Bank Economic Review 17(1) 51-88

Born P amp Viscusi W K (2006) The catastrophic effects of natural disasters on insurance markets

Journal of Risk and Uncertainty 33(1-2) 55-72

Braun M amp Muermann A (2004) The impact of regret on the demand for insurance Journal of

Risk and Insurance 71(4) 737-767

Browne M J amp Hoyt R E (2000) The demand for flood insurance empirical evidence Journal of

Risk and Uncertainty 20(3) 291-306

Browne M J amp Kim K (1993) An international analysis of life insurance demand Journal of Risk

and Insurance 616-634

Bruin J (2006) newtest command to compute new test UCLA Statistical Consulting Group

httpwwwatsuclaedustatstataadoanalysis

Camerer C amp Kunreuther H (1989) Experimental markets for insurance Journal of Risk and

Uncertainty 2(3) 265-299

Cohen M Etner J amp Jeleva M (2008) Dynamic decision making when risk perception depends

on past experience Theory and Decision 64(2-3) 173-192

Dragos S L (2014) Life and non-life insurance demand the different effects of influence factors in

emerging countries from Europe and Asia Economic Research-Ekonomska Istraživanja

27(1) 169-180

Dumm R Nyce C Sirmans G S amp Smersh G (2012) The Capitalization of Homeowners

Insurance Premiums in House Prices Retrieved from

Dumm R E Eckles D L Nyce C amp Volkman-Wise J (2015) Demand for Catastrophe

Insurance and the Representative Heuristic

Dzaja I (2013) The effect of social and demographic factors on life insurance demand in Croatia

International Journal of Business and Social Science 4(9)

Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

the US Department of Economics University of California at Berkeley 47

Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

insurance for disaster-type risks experimental evidence Journal of Risk and Uncertainty

20(3) 271-289

Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

Economic association 6(6) 1109-1150

Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

scales Multivariate Behavioral Research 14(2) 255-269

Kirsch I (1986) Early research on self-efficacy What we already know without knowing we knew

Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

protection Journal of Risk and Uncertainty 33(1-2) 73-100

Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

and Insurance 206-220

Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

decision processes Journal of Economic Behavior amp Organization 26(3) 337-352

Page 44 of 45

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Gallagher J (2010) Learning about an infrequent event Evidence from flood insurance take-up in

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Ganderton P T Brookshire D S McKee M Stewart S amp Thurston H (2000) Buying

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Guiso L amp Paiella M (2008) Risk aversion wealth and background risk Journal of the European

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Hwang T amp Gao S (2003) The determinants of the demand for life insurance in an emerging

economy-the case of China Managerial Finance 29(56) 82-96

Janson S amp Vegelius J (1979) On generalizations of the G index and the phi coefficient to nominal

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Journal of Social and Clinical Psychology 4(3) 339-358

Kousky C Luttmer E F amp Zeckhauser R J (2006) Private investment and government

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Kunreuther H (1984) Causes of underinsurance against natural disasters Geneva Papers on Risk

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Kunreuther H Meszaros J Hogarth R M amp Spranca M (1995) Ambiguity and underwriter

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